Range (statistics)
In the descriptive statistics
Descriptive statistics
Descriptive statistics quantitatively describe the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics , in that descriptive statistics aim to summarize a data set, rather than use the data to learn about the population that the data are...

, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation (sample minimum) from the greatest (sample maximum) and provides an indication of statistical dispersion
Statistical dispersion
In statistics, statistical dispersion is variability or spread in a variable or a probability distribution...


It is measured in the same units as the data. Since it only depends on two of the observations, it is a poor and weak measure of dispersion except when the sample size is large.

For a population, the range is greater than or equal to twice the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

, with equality only for the coin toss (Bernoulli distribution with p = ½).

The range, in the sense of the difference between the highest and lowest scores, is also called the crude range. When a new scale for measurement is developed, then a potential maximum or minimum will emanate from this scale. This is called the potential (crude) range. Of course this range should not be chosen too small, in order to avoid a ceiling effect
Ceiling effect
The term ceiling effect has two distinct meanings, referring to the level at which an independent variable no longer has an effect on a dependent variable, or to the level above which variance in an independent variable is no longer measured or estimated...

. When the measurement is obtained, the resulting smallest or greatest observation, will provide the observed (crude) range.

The midrange point, i.e. the point halfway between the two extremes, is an indicator of the central tendency
Central tendency
In statistics, the term central tendency relates to the way in which quantitative data is clustered around some value. A measure of central tendency is a way of specifying - central value...

 of the data. Again it is not particularly robust for small samples.

See also

  • Sample maximum and minimum
    Sample maximum and minimum
    In statistics, the maximum and sample minimum, also called the largest observation, and smallest observation, are the values of the greatest and least elements of a sample....

  • Interquartile range
    Interquartile range
    In descriptive statistics, the interquartile range , also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles...

  • Studentized range
  • Peirce's criterion
    Peirce's criterion
    In robust statistics, Peirce's criterion is a rule for eliminating outliers from data sets, which was devised by Benjamin Peirce.-The problem of outliers:...

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